Hobart :

for me MONA is a must see although some people are put off by various art pieces.(even to the point of lawsuits). Also the dedicated ferry to and from MONA is more fun and I think you might need to book ahead for some exhibitions

Port Arthur is great. Plan an entire day there, have picnic and take the boat to the Isle of the Dead for an interesting guided tour of the penal colony cemetery.

Some of my favourite food and drink in Hobart:

Bar Wa Izakaya , a super fun Japanese restaurant

Urban Greek, delicious food and great service

Landscape grill for excellent steak

The Den Salamanca, cozy whiskey/cocktail bar to chill out after you hit the market. The food is good as well.

Moto Vecchia cafe, for nice coffee and brekkie. They are super friendly there. It’s just across the river.

Further afield: King Solomons cave in Liena is really cool guided tour and worth the drive. Stop in Mumma Buzz’s Cafe in Deloraine for excellent egg and bacon roll

Cataract Gorge in Launceston is a beautiful bike or walk track

If we take the Spirit, we normally book the overnight trip.

The Botanical Gardens. The Japanese garden is exquisite.

Port Arthur is pretty interesting if you've never been and there's an animal sanctuary not far from there too.

there are some pretty nice forest lands /parks

museums and zoos

beaches of course